Abstract

A previous layer-by-layer multilayer design method [J. Opt. Soc. Am. A 19, 385 (2002)] is completed by adding the possibility of alternating layers with fixed thicknesses along with layers whose thicknesses are optimized for the largest possible reflectance at a desired wavelength. The previous algorithm did not allow for layers with fixed thicknesses. The current formalism is particularly suited for a multilayer design in which barrier layers of given thicknesses are used to prevent diffusion and/or reaction between the multilayer constituents. The design method is also useful both when intermixing zones develop at multilayer interfaces and when capping layers are used. The algorithm allows the design of multilayers with complex barrier layers with any number of layers of any optical constants. The optimization can be performed either for normal incidence or for nonnormal incidence with either s- or p-polarized radiation. The completed method provides a fast and accurate procedure for multilayer optimization regardless of the number of different materials used in the multilayer. The optimum layer thickness is determined by means of functions suitable for implementation in a computer code. The performance of the current algorithm is exemplified through the design of Si/Mo multilayers with intermixing layers or with barrier layers that are optimized for the largest reflectance at 13.4 nm. The use of specific barrier layers on each multilayer interface is also discussed.

© 2004 Optical Society of America

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  1. E. Spiller, ed., Soft X-Ray Optics (SPIE Press, Bellingham, Wash., 1994), p. 143.
  2. J. I. Larruquert, “New layer-by-layer multilayer design method,” J. Opt. Soc. Am. A 19, 385–390 (2002).
    [CrossRef]
  3. M. Yamamoto, T. Namioka, “Layer-by-layer design method for soft-x-ray multilayers,” Appl. Opt. 31, 1622–1630 (1992).
    [CrossRef] [PubMed]
  4. J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
    [CrossRef]
  5. T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
    [CrossRef]
  6. See, for instance, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).
  7. D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990), and references therein.
    [CrossRef]
  8. S. Braun, H. Mai, M. Moss, R. Scholz, A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys., Part 1 41, 4074–4081 (2002).
    [CrossRef]
  9. D. G. Stearns, R. S. Rosen, “High-performance multilayer mirrors for soft x-ray projection lithography,” in Multilayer Optics for Advanced X-Ray Applications, N. M. Ceglio, ed., Proc. SPIE1547, 2–13 (1991).
    [CrossRef]
  10. http://www-cxro.lbl.gov/optical_constants .
  11. J. I. Larruquert, “Sub-quarterwave multilayers with enhanced reflectance at 13.4 and 11.3 nm,” Opt. Commun. 206, 259–273 (2002).
    [CrossRef]
  12. H. Takenaka, H. Ito, T. Haga, T. Kawamura, “Design and fabrication of highly heat-resistant Mo/Si multilayer soft x-ray mirrors with interleaved barrier layers,” J. Synchrotron Radiat. 5, 708–710 (1998).
    [CrossRef]
  13. T. Feigl, H. Lauth, S. Yulin, N. Kaiser, “Heat resistance of EUV multilayer mirrors for long-time applications,” Microelectron. Eng. 57–58, 3–8 (2001).
    [CrossRef]
  14. S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
    [CrossRef]
  15. M. Singh, J. J. M. Braat, “Design of multilayer extreme-ultraviolet mirrors for enhanced reflectivity,” Appl. Opt. 39, 2189–2197 (2000).
    [CrossRef]
  16. J. I. Larruquert, “Reflectance enhancement in the extreme ultraviolet and soft x-rays by means of multilayers with more than two materials,” J. Opt. Soc. Am. A 19, 391–397 (2002).
    [CrossRef]
  17. T. L. Lee, L. J. Chen, “Interfacial reactions in ultrahigh vacuum deposited Y-Si multilayer thin films,” J. Appl. Phys. 75, 2007–2014 (1994).
    [CrossRef]

2002 (5)

J. I. Larruquert, “New layer-by-layer multilayer design method,” J. Opt. Soc. Am. A 19, 385–390 (2002).
[CrossRef]

S. Braun, H. Mai, M. Moss, R. Scholz, A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys., Part 1 41, 4074–4081 (2002).
[CrossRef]

J. I. Larruquert, “Sub-quarterwave multilayers with enhanced reflectance at 13.4 and 11.3 nm,” Opt. Commun. 206, 259–273 (2002).
[CrossRef]

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

J. I. Larruquert, “Reflectance enhancement in the extreme ultraviolet and soft x-rays by means of multilayers with more than two materials,” J. Opt. Soc. Am. A 19, 391–397 (2002).
[CrossRef]

2001 (1)

T. Feigl, H. Lauth, S. Yulin, N. Kaiser, “Heat resistance of EUV multilayer mirrors for long-time applications,” Microelectron. Eng. 57–58, 3–8 (2001).
[CrossRef]

2000 (1)

1998 (1)

H. Takenaka, H. Ito, T. Haga, T. Kawamura, “Design and fabrication of highly heat-resistant Mo/Si multilayer soft x-ray mirrors with interleaved barrier layers,” J. Synchrotron Radiat. 5, 708–710 (1998).
[CrossRef]

1996 (1)

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

1995 (1)

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

1994 (1)

T. L. Lee, L. J. Chen, “Interfacial reactions in ultrahigh vacuum deposited Y-Si multilayer thin films,” J. Appl. Phys. 75, 2007–2014 (1994).
[CrossRef]

1992 (1)

1990 (1)

D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990), and references therein.
[CrossRef]

Alameda, J. B.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

Artzner, -G. E.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Au, B.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Bajt, S.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

Barbee, T. W.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

Braat, J. J. M.

Braun, S.

S. Braun, H. Mai, M. Moss, R. Scholz, A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys., Part 1 41, 4074–4081 (2002).
[CrossRef]

Brunaud, J.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Catura, R. C.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Ceglio, N. M.

D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990), and references therein.
[CrossRef]

Chauvineau, J. P.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Chen, L. J.

T. L. Lee, L. J. Chen, “Interfacial reactions in ultrahigh vacuum deposited Y-Si multilayer thin films,” J. Appl. Phys. 75, 2007–2014 (1994).
[CrossRef]

Cheng, Y.

D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990), and references therein.
[CrossRef]

Clette, F.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Clift, W. M.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

Cugnon, P.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Defise, J. M.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Delaboudinière, J.-P.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Dere, K. P.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Feigl, T.

T. Feigl, H. Lauth, S. Yulin, N. Kaiser, “Heat resistance of EUV multilayer mirrors for long-time applications,” Microelectron. Eng. 57–58, 3–8 (2001).
[CrossRef]

Flannery, B. P.

See, for instance, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).

Folta, J. A.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

Gabriel, A. H.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Gurman, J. B.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Haga, T.

H. Takenaka, H. Ito, T. Haga, T. Kawamura, “Design and fabrication of highly heat-resistant Mo/Si multilayer soft x-ray mirrors with interleaved barrier layers,” J. Synchrotron Radiat. 5, 708–710 (1998).
[CrossRef]

Hochedez, J. F.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Howard, R. A.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Ikeda, K.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Ito, H.

H. Takenaka, H. Ito, T. Haga, T. Kawamura, “Design and fabrication of highly heat-resistant Mo/Si multilayer soft x-ray mirrors with interleaved barrier layers,” J. Synchrotron Radiat. 5, 708–710 (1998).
[CrossRef]

Jamar, C.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Kaiser, N.

T. Feigl, H. Lauth, S. Yulin, N. Kaiser, “Heat resistance of EUV multilayer mirrors for long-time applications,” Microelectron. Eng. 57–58, 3–8 (2001).
[CrossRef]

Kaufmann, B.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

Kawamura, T.

H. Takenaka, H. Ito, T. Haga, T. Kawamura, “Design and fabrication of highly heat-resistant Mo/Si multilayer soft x-ray mirrors with interleaved barrier layers,” J. Synchrotron Radiat. 5, 708–710 (1998).
[CrossRef]

Kreplin, R.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Kunieda, H.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Larruquert, J. I.

Lauth, H.

T. Feigl, H. Lauth, S. Yulin, N. Kaiser, “Heat resistance of EUV multilayer mirrors for long-time applications,” Microelectron. Eng. 57–58, 3–8 (2001).
[CrossRef]

Lee, T. L.

T. L. Lee, L. J. Chen, “Interfacial reactions in ultrahigh vacuum deposited Y-Si multilayer thin films,” J. Appl. Phys. 75, 2007–2014 (1994).
[CrossRef]

Lemen, J. R.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Leson, A.

S. Braun, H. Mai, M. Moss, R. Scholz, A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys., Part 1 41, 4074–4081 (2002).
[CrossRef]

Mai, H.

S. Braun, H. Mai, M. Moss, R. Scholz, A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys., Part 1 41, 4074–4081 (2002).
[CrossRef]

Marioge, J. P.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Maucherat, A.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Michels, D. J.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Miller, F.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Misaki, K.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Moses, J. D.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Moss, M.

S. Braun, H. Mai, M. Moss, R. Scholz, A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys., Part 1 41, 4074–4081 (2002).
[CrossRef]

Nakamura, M.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Namioka, T.

Neupert, W. M.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Press, W. H.

See, for instance, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).

Rochus, P.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Rosen, R. S.

D. G. Stearns, R. S. Rosen, “High-performance multilayer mirrors for soft x-ray projection lithography,” in Multilayer Optics for Advanced X-Ray Applications, N. M. Ceglio, ed., Proc. SPIE1547, 2–13 (1991).
[CrossRef]

Scholz, R.

S. Braun, H. Mai, M. Moss, R. Scholz, A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys., Part 1 41, 4074–4081 (2002).
[CrossRef]

Shing, L.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Singh, M.

Song, X. Y.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Spiller, E. A.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

Stearns, D. G.

D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990), and references therein.
[CrossRef]

D. G. Stearns, R. S. Rosen, “High-performance multilayer mirrors for soft x-ray projection lithography,” in Multilayer Optics for Advanced X-Ray Applications, N. M. Ceglio, ed., Proc. SPIE1547, 2–13 (1991).
[CrossRef]

Stearns, M. B.

D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990), and references therein.
[CrossRef]

Stern, R. A.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Stith, J. H.

D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990), and references therein.
[CrossRef]

Takenaka, H.

H. Takenaka, H. Ito, T. Haga, T. Kawamura, “Design and fabrication of highly heat-resistant Mo/Si multilayer soft x-ray mirrors with interleaved barrier layers,” J. Synchrotron Radiat. 5, 708–710 (1998).
[CrossRef]

Takizawa, Y.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Teukolsky, S. A.

See, for instance, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).

Van Dessel, E. L.

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Vetterling, W. T.

See, for instance, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).

Yamaguchi, A.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Yamamoto, M.

Yamashita, K.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Yamazaki, T.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Yoshikawa, L.

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

Yulin, S.

T. Feigl, H. Lauth, S. Yulin, N. Kaiser, “Heat resistance of EUV multilayer mirrors for long-time applications,” Microelectron. Eng. 57–58, 3–8 (2001).
[CrossRef]

Appl. Opt. (2)

J. Appl. Phys. (2)

T. L. Lee, L. J. Chen, “Interfacial reactions in ultrahigh vacuum deposited Y-Si multilayer thin films,” J. Appl. Phys. 75, 2007–2014 (1994).
[CrossRef]

D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990), and references therein.
[CrossRef]

J. Electron Spectrosc. Relat. Phenom. (1)

T. Yamazaki, Y. Takizawa, H. Kunieda, K. Yamashita, K. Ikeda, K. Misaki, M. Nakamura, L. Yoshikawa, A. Yamaguchi, “Normal incidence multilayer telescope for galactic EUV observation,” J. Electron Spectrosc. Relat. Phenom. 80, 299–302 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Synchrotron Radiat. (1)

H. Takenaka, H. Ito, T. Haga, T. Kawamura, “Design and fabrication of highly heat-resistant Mo/Si multilayer soft x-ray mirrors with interleaved barrier layers,” J. Synchrotron Radiat. 5, 708–710 (1998).
[CrossRef]

Jpn. J. Appl. Phys., Part 1 (1)

S. Braun, H. Mai, M. Moss, R. Scholz, A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys., Part 1 41, 4074–4081 (2002).
[CrossRef]

Microelectron. Eng. (1)

T. Feigl, H. Lauth, S. Yulin, N. Kaiser, “Heat resistance of EUV multilayer mirrors for long-time applications,” Microelectron. Eng. 57–58, 3–8 (2001).
[CrossRef]

Opt. Commun. (1)

J. I. Larruquert, “Sub-quarterwave multilayers with enhanced reflectance at 13.4 and 11.3 nm,” Opt. Commun. 206, 259–273 (2002).
[CrossRef]

Opt. Eng. (1)

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[CrossRef]

Sol. Phys. (1)

J.-P. Delaboudinière, -G. E. Artzner, J. Brunaud, A. H. Gabriel, J. F. Hochedez, F. Miller, X. Y. Song, B. Au, K. P. Dere, R. A. Howard, R. Kreplin, D. J. Michels, J. D. Moses, J. M. Defise, C. Jamar, P. Rochus, J. P. Chauvineau, J. P. Marioge, R. C. Catura, J. R. Lemen, L. Shing, R. A. Stern, J. B. Gurman, W. M. Neupert, A. Maucherat, F. Clette, P. Cugnon, E. L. Van Dessel, “EIT: Extreme-Ultraviolet Imaging Telescope for the SOHO Mission,” Sol. Phys. 162, 291–312 (1995).
[CrossRef]

Other (4)

E. Spiller, ed., Soft X-Ray Optics (SPIE Press, Bellingham, Wash., 1994), p. 143.

D. G. Stearns, R. S. Rosen, “High-performance multilayer mirrors for soft x-ray projection lithography,” in Multilayer Optics for Advanced X-Ray Applications, N. M. Ceglio, ed., Proc. SPIE1547, 2–13 (1991).
[CrossRef]

http://www-cxro.lbl.gov/optical_constants .

See, for instance, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).

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Figures (7)

Fig. 1
Fig. 1

Ninth power of the reflectance at 13.4 nm for Si/Mo multilayers with silicide intermixing layers. The multilayers are optimized for the largest reflectance at 13.4 nm at normal incidence. “Optimized” refers to the multilayer calculated with the current algorithm. CP (constant periods) refers to the multilayer calculated starting with Γ=0.41 with further silicide insertion. OCP (optimized constant periods) refers to the multilayer in which xSi and xMo (Si and Mo layer thicknesses, respectively; xSi and xMo are constant throughout the multilayer) were optimized independently for the largest reflectance at 13.4 nm.

Fig. 2
Fig. 2

Layer thicknesses of Si/Mo multilayers with silicide intermixing layers. The multilayers are optimized for the largest reflectance at 13.4 nm at normal incidence. The intermixing layers of MoSi2 are 0.7 nm and 1.2 nm thick at the Si-on-Mo and Mo-on-Si interfaces, respectively, and are not displayed. The crosses and circles refer to the Si and Mo layers, respectively, of the multilayer calculated with the current optimization method. Symbols 1 and 2 refer to the Si and Mo layers, respectively, of the multilayer with constant periods calculated starting with Γ=0.41 with further silicide insertion. Symbols 3 and 4 refer to the Si and Mo layers, respectively, of the multilayer with optimized constant periods.

Fig. 3
Fig. 3

Thickness differences between the (Si/Mo)40/Si and (Si/0.7-nm MoSi2/Mo/1.2-nm MoSi2)40/Si multilayers. The two were optimized with the current algorithm. Layer numbers are assigned by ignoring the silicide layer numbers. The outermost Si layer is not displayed.  

Fig. 4
Fig. 4

Ninth power of the reflectance at 13.4 nm for Si/Mo multilayers with 0.4-nm-thick B4C barrier layers. The multilayers are optimized for the largest reflectance at 13.4 nm at normal incidence. “Optimized” refers to the multilayer calculated with the current optimization method. OCP (optimized constant periods) refers to the multilayer in which xSi and xMo (Si and Mo layer thicknesses, respectively; xSi and xMo are constant throughout the multilayer) were optimized independently for the largest reflectance at 13.4 nm.

Fig. 5
Fig. 5

Layer thicknesses of Si/Mo multilayers with B4C barrier layers. The multilayers are optimized for the largest reflectance at 13.4 nm at normal incidence. The barrier layers are 0.4 nm thick at the two interfaces and are not displayed. The crosses and circles refer to the Si and Mo layers, respectively, of the multilayer calculated with the current optimization method. Symbols 1 and 2 refer to the Si and Mo layers, respectively, of the multilayer with optimized constant periods.

Fig. 6
Fig. 6

Thickness differences between the (Si/Mo)40/Si and (Si/0.4-nm B4C/Mo/0.4-nm B4C)40/Si multilayers. The two were optimized with the current algorithm. Layer numbers are assigned by ignoring the barrier layer numbers. The outermost Si layer is not displayed.

Fig. 7
Fig. 7

Optical constants of Mo, Si, and other low-absorption materials at 13.4 nm.

Tables (4)

Tables Icon

Table 1 Density and Optical Constants at 13.4 nm for Several Materials

Tables Icon

Table 2 Reflectance at 13.4 nm, Ninth Power of That Reflectance, and the Latter Integrated through the Band for Different Designs of Si/Mo Multilayers with a 0.7-nm-Thick Silicide Layer at the Si-on-Mo Interface and a 1.2-nm-Thick Silicide Layer at the Mo-on-Si Interface a

Tables Icon

Table 3 Reflectance at 13.4 nm, Ninth Power of That Reflectance, and the Latter Integrated through the Band for Two Si/Mo Multilayers with 0.4 nm-Thick B4C Barrier Layers at Both the Si-on-Mo and Mo-on-Si Interfaces a

Tables Icon

Table 4 Reflectance at 13.4 nm for Si/Mo Multilayers with Several Barrier Layer Materials a

Equations (32)

Equations on this page are rendered with MathJax. Learn more.

rj-1=fj-1+rjexp βj1+fj-1+rjexp βj,j=lto1,
rl=fl
βj=4πiNjcos θj xjλ,
Njcos θj=(Nj2-N02sin2 θ0)1/2.
R0=r0*r0.
Rxh(i)max=0,i=1tom;
(-1)idet1,i2Rxh(k1)xh(k2)max>0,i=1tom,
Rxh(1)max=2 Rer0*r0xh(1)=0,
Rxh(i)max=2 Rer0*r0xh(i)=-2 Imr0*r0xh(1)×Imrh(i-1)-1xh(i)/rh(i-1)-1xh(i-1)×k=2i-1Rerh(k-1)-1xh(k)/rh(k-1)-1xh(k-1)=0,
i=2tom,
Rer0*r0xh(1)=0,i=1,
Imrh(i-1)-1xh(i)/rh(i-1)-1xh(i-1)=0,i=2tom.
Rer0*r0xh(1)=Rer0*r0x1r0x2r0x1  r1x3r1x2  rh(1)-2xh(1)rh(1)-2xh(1)-1  =-4πλR0N0cos θ0Im(U1),
Imrh(i-1)-1xh(i)rh(i-1)-1xh(i-1)  
=Imrh(i-1)-1xh(i-1)+1rh(i-1)-1xh(i-1)  rh(i-1)xh(i-1)+2rh(i-1)xh(i-1)+1rh(i)-2xh(i)rh(i)-2xh(i)-1  =Im(Ui),i=2tom,
Ui=j=h(i-1)+1h(i)uj,i=1tom,
uj=rj-2xjrj-2xj-1  =Njcos θjNj-1cos θj-1(1-fj-12)rjexp βj(fj-1+rjexp βj)(1+fj-1rjexp βj).
Im(Ui)=0,i=1tom.
ImUixik=1i-1Re(Uk)>0,i=1tom.
Rep=h(i-1)+1h(i)wpq=h(i-1)+1p-1uqk=1i-1Re(Uk)>0,
i=1tom,
wp=Np-1cos θp-1fp-1[1-rp2exp(2βp)](1-fp-12)rpexp βp,
p=1tol.
ImUixi= Im(Ui)xi,i=1tom,
Im(Ui)=0 Im(Ui)xik=1i-1Re(Uk)>0,i=1tom.
Im(Ui)=0, &  Im(Ui)xi>0,i=1tom,
Re(Ui)>0,i=1tom.
Im(Ui)=0 Im(Ui)xi>0,i=1tom.
ΔxSi=2 ρMoSi2MSiρSiMMoSi2 xMoSi2,ΔxMo=ρMoSi2MMoρMoMMoSi2 xMoSi2,
ΔΛ=xMoSi2-ΔxSi-ΔxMo=-0.74nm
PSD=xMoSi2nMoSi2-ΔxSinSi-ΔxMonMoxSinSi+xMonMo π.
Im(ΔNi/ΔNi-1)<0,

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